For example, a computer with the mass of the entire Earth operating at the Bremermann's limit could perform approximately 1075 mathematical computations per second. If one assumes that a cryptographic key can be tested with only one operation, then a typical 128-bit key could be cracked in under 10−36 seconds. However, a 256-bit key (which is already in use in some systems) would take about two minutes to crack. Using a 512-bit key would increase the cracking time to approaching 1072 years, without increasing the time for encryption by more than a constant factor (depending on the encryption algorithms used).

The limit has been further analysed in later literature as the maximum rate at which a system with energy spread ΔE{\displaystyle \Delta E} can evolve into an orthogonal and hence distinguishable state to another, Δt=πℏ2ΔE{\displaystyle \Delta t={\frac {\pi \hbar }{2\Delta E}}}.[3][4] In particular, Margolus and Levitin has shown that a quantum system with average energy E takes at least time Δt=πℏ2E{\displaystyle \Delta t={\frac {\pi \hbar }{2E}}} to evolve into an orthogonal state.[5]
However, it has been shown that access to quantum memory in principle allows computational algorithms that require arbitrarily small amount of energy/time per one elementary computation step.[6][7]